# If the 9th term of an A.P. is zero then show that the 29th term is twice the 19th term.

Now, By using nth term of an A.P. formula

tn = a + (n – 1)d

where n = no. of terms

a = first term

d = common difference

tn = nth terms

Given: t9 = 0

t9 = a + (9 – 1)d

0 = a + 8d

a = – 8d

To Show: t29 = 2× t19

Now,

t29 = a + (29 – 1)d

t29 = a + 28d

t29 = – 8d + 28d = 20 d (since, a = – 8d )

t29 = 20 d

t29 = 2 × 10 d ….(1)

Also,

t19 = a + (19 – 1)d

t19 = a + 18d

t19 = – 8d + 18d = 10 d (since, a = – 8d )

t19 = 10 d …..(2)

From eq. (1) and eq. (2) we get,

t29 = 2× t19

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Champ Quiz | Arithmetic Progression30 mins  Champ Quiz | Arithmetic Progression34 mins  Quiz | Arithmetic Progression44 mins  Smart Revision | Arithmetic Progression47 mins  Smart Revision | General Term of an A.P44 mins  Master Arithmetic Progression36 mins  Lets Check Your Knowledge in A.P.49 mins  Quiz on Arithmetic Progression Quiz32 mins  Get to Know About Geometric Progression41 mins  NCERT | Solving Questions on Introduction of A.P42 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 